The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.
MEMS (micro-electromechanical system) gyroscopes, such as the silicon disc resonator gyroscope (DRG) are typically operated with a single mechanical resonant frequency on both the drive and sense axes of the DRG. Due to manufacturing variations, there is typically a frequency offset between the two vibrational modes of the DRG used for driving and sensing the motion, respectively, that must be corrected by a means such as electrostatic tuning or mass trimming to bring the two frequencies into coincidence. The inventors have discovered that during etching of the resonator pattern on the resonator wafer of the DRG, asymmetric conduction of heat during the etching process can cause subtle dimensional variations in the arcuate slots created during the etching process. More specifically, the inventors have discovered that during the etching process, hotter regions of the resonator wafer tend to etch faster and have more mask undercut than cooler areas. This difference in temperature can result in etching that produces arcuate slots in the resonator wafer that are either slightly larger or smaller in cross sectional dimension, than a desired design dimension. Put differently, the difference in various regions of the resonator wafer during the etching process can cause geometric asymmetry of the resulting slots, and thus the beams that are formed in the resonator wafer. These differences (i.e., variations) in cross sectional dimension for the slots result in beams being created that can be either slightly thicker than desired, or slightly thinner than desired, which introduces a variation in the mechanical compliance of the beams, and hence vibrational frequency, for different radial orientations of the gyroscope. This variation in sensitivity is manifested in the above-mentioned frequency offset that is present between the two vibrational modes of the DRG used for drive and sense, respectively, that must be corrected. Slight differences in beam thickness, on the order of tens of nanometers, can give rise to frequency offsets of order 20-40 Hz for DRG structures designed for a resonant frequency of order 14 kHz. This asymmetry can arise even for a fully symmetric resonator pattern.
Correction of the frequency offset introduces additional cost and complexity into the DRG, or into its manufacture. Correction typically has been accomplished by subsequent electronic tuning of the DRG or physically trimming portions of the resonator wafer to bring the two vibrational modes into coincidence. Electronic tuning adds to complexity in the electronic circuitry, and tuning voltage instability can degrade apparent device performance. Physical trimming of the resonator requires additional processing, such as laser trimming, that is both expensive and time consuming.